# On a Bernoulli problem with geometric constraints

Antoine Laurain; Yannick Privat

ESAIM: Control, Optimisation and Calculus of Variations (2012)

- Volume: 18, Issue: 1, page 157-180
- ISSN: 1292-8119

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topLaurain, Antoine, and Privat, Yannick. "On a Bernoulli problem with geometric constraints." ESAIM: Control, Optimisation and Calculus of Variations 18.1 (2012): 157-180. <http://eudml.org/doc/221908>.

@article{Laurain2012,

abstract = {A Bernoulli free boundary problem with geometrical constraints is studied. The domain Ω is constrained to lie in the half space determined by x1 ≥ 0 and its boundary to contain a segment of the hyperplane \{x1 = 0\} where non-homogeneous Dirichlet conditions are imposed. We are then looking for the solution of a partial differential equation satisfying a Dirichlet and a Neumann boundary condition simultaneously on the free boundary. The existence and uniqueness of a solution have already been addressed and this paper is devoted first to the study of geometric and asymptotic properties of the solution and then to the numerical treatment of the problem using a shape optimization formulation. The major difficulty and originality of this paper lies in the treatment of the geometric constraints. },

author = {Laurain, Antoine, Privat, Yannick},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Free boundary problem; Bernoulli condition; shape optimization; free boundary problem},

language = {eng},

month = {2},

number = {1},

pages = {157-180},

publisher = {EDP Sciences},

title = {On a Bernoulli problem with geometric constraints},

url = {http://eudml.org/doc/221908},

volume = {18},

year = {2012},

}

TY - JOUR

AU - Laurain, Antoine

AU - Privat, Yannick

TI - On a Bernoulli problem with geometric constraints

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2012/2//

PB - EDP Sciences

VL - 18

IS - 1

SP - 157

EP - 180

AB - A Bernoulli free boundary problem with geometrical constraints is studied. The domain Ω is constrained to lie in the half space determined by x1 ≥ 0 and its boundary to contain a segment of the hyperplane {x1 = 0} where non-homogeneous Dirichlet conditions are imposed. We are then looking for the solution of a partial differential equation satisfying a Dirichlet and a Neumann boundary condition simultaneously on the free boundary. The existence and uniqueness of a solution have already been addressed and this paper is devoted first to the study of geometric and asymptotic properties of the solution and then to the numerical treatment of the problem using a shape optimization formulation. The major difficulty and originality of this paper lies in the treatment of the geometric constraints.

LA - eng

KW - Free boundary problem; Bernoulli condition; shape optimization; free boundary problem

UR - http://eudml.org/doc/221908

ER -

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